The present invention relates to the broad field of FM waveform generation and more particularly, to a sampling linearizer which provides the sampling rate sufficient to control the accuracy of the FM waveform to that required for applications in very high resolution mapping type radar systems, for example.
In most cases, high resolution mapping type radar systems employ FM (chirp) waveform generation, usually of the linear frequency rate of change type, to achieve their specified range resolution requirements. Normally, very high resolution radars require waveforms with a bandwidth of 1,000 MHZ or greater, with time-bandwidth products of perhaps 100,000. The accuracy requirement for these high bandwidth type linear frequency rate of change type FM waveform generators is generally severe especially in air-ground radar mapping systems which map large swaths. These air-ground radar mapping systems may, in some cases, be specified to have 50 dB more stringent linearity requirements than ground-based radar systems, for example. To achieve an accuracy requirement of this nature, most FM waveform generators have included some type of servo loop control.
The most common type of servo loop control for controlling the accuracy of the desired frequency rate of change of the generated FM waveform in chirp generation employs sampling techniques and is commonly referred to as a sampling linearizer. A schematic block diagram of a typical active chirp generator utilizing a sampling linearizer is shown in FIG. 1. Typically, a FM generator 10 of the linear frequency rate of change type, for example, generates a FM microwave signal 12 at a desired frequency rate of change as governed by a tuning waveform signal 14. The desired waveform 12 which may be expressed by the well-known equation F=F.sub.O +kt is coupled to one input of a conventional mixer 15 wherein it is compared to a reference microwave signal 16 which is generated from a stable microwave oscillator 18. The frequency of the reference signal 16 is usually tuned to the initial ramp frequency F.sub.O of the desired FM waveform 12. During the dead time period just prior to the start of generation of the liner linear waveform ramp at 12, the FM generator 10 is normally phase locked to the output signal F.sub. O of stable oscillator 18. In response to the generated FM ramp signal 12, the mixer 15 generates a signal 20 which is depicted by the graph of FIG. 2. The solid line 22 in the graph of FIG. 2 which may be expressed by F=kt is the desired linear FM waveform 12 beat down to baseband by mixer 15. The dotted curve 24 of the graph of FIG. 2 is representative of an exaggerated non-linear FM generated signal which needs linearization.
A synchronizer 26 which is normally synchronized to the stable oscillator 18 controls a conventional sampler 28 to sample-and-hold the signal 20 for predetermined sampling intervals T.sub.S. The times at which the signal 20 is sampled are generally selected to be at 2.pi. multiples of the phase of the desired FM waveform (refer to FIG. 3). Accordingly, the sampling interval T.sub.S is selected such that if the generated FM waveform at 12 is linear and has the correct slope, the sampler output 29 will always be substantially zero as exhibited by the points 30, 32 and 34 corresponding to sampling time T.sub.S, 2T.sub.S and 3T.sub.S in FIG. 3. If the FM waveform at 12 has an inaccuracy such as a deviation from the desired slope k or non-linearities similar to that shown in FIG. 2, an output signal over line 29 is generated at some appropriate value for each sample to govern a linearizing servo controller 36, generally well known in the art, to generate the appropriate compensation in the tuning signal 14 which, in turn, controls the accuracy of the generated FM waveform 12 and forces the output signal over line 29 to zero.
For a more detailed description of some sampling linearizers exemplary of the type described above, reference is made to the following U.S. Pat. Nos. 3,382,460 entitled "Linearly Swept Frequency Generator" issued to D. Blitz et al on May 7, 1968; 3,699,448 entitled "Precision Generation Of Linear F.M. Signal" issued to G. L. Martin et al on Oct. 17, 1972; and 4,038,612 entitled "Swept Oscillator Automatic Linearizer" issued to R. P. Barofka et al on July 26, 1977.
In analyzing the available performance of these known type sampling linearizers, it is first identified that the desired frequency of the FM generated waveform may be expressed by EQU F(t)=F.sub.O +kt (1')
where F.sub.O is the initial frequency of the frequency sweep, k is the slope (Hz/second), and t is the accumulated time after waveform initialization, T.sub.O. If the oscillator 18 is set at the stable frequency F.sub.O, it follows that the desired waveform phase .phi. generated at the output of mixer 15 may be expressed by EQU .phi.(t)=+.pi.kt.sup.2 ( 2')
If the sampling times .alpha.T.sub.S are always selected to be multiples of 2.pi. of the desired FM waveform, it can be shown that: EQU .phi.(.alpha.)=2.pi..alpha..sup.2 =.pi.k (.alpha.T.sub.S).sup.2 ( 3')
thus, solving equation (3') for T.sub.S, we find that EQU T.sub.S =.sqroot.2/k. (4')
Thus, the sampling rate 1/T.sub.S is uniquely determined by the waveform slope k.
As is well known in the pertinent art, the sampling period T.sub.S introduces a transport delay of T.sub.S /2 into the servo control loop of the sampling linearizer, and this delay limits the loop bandwidth F.sub.SL of the servo control. Type II servo controllers are usually used for linearization. To stabilize these servo control loops when a time delay is introduced such as with the sampler, it is generally necessary to limit the excess phase effected by the sampler to approximately .pi./8 at the servo loop bandwidth frequency F.sub.SL. In so doing, it may be shown that the bandwidth F.sub.SL is equated to 1/8 T.sub.S. If equation (4') is substituted for T.sub.S, the loop bandwidth may be expressed as EQU F.sub.SL =1/8.sqroot. k/2. (5')
Unfortunately, this bandwidth has been found to be inadequate, in some cases, to provide the required accuracy and transient response characteristics for some applications such as the high resolution mapping type radars. A more desirable mechanization may be one which maintains the simplicity of the conventional sampling linearizer, but which provides substantially greater sampling rate and servo bandwidth.